非可逆对称性与顶点算子代数外自同构
Non-invertible symmetry and vertex operator algebra outer-automorphism
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中文总结 AI 辅助
该研究论证$\boldsymbol{\textit{N}=4}$超杨-米尔斯理论的非可逆对称性对应相关顶点算子代数的外自同构，通过大$\boldsymbol{\textit{N}}$极限和融合规则匹配验证了该结论，且“带电”Schur指标与外自同构扭转的真空特征相符。
中文摘要 AI 辅助
我们论证，通过结合S对偶、半空间规范群和R对称扭转得到的$\boldsymbol{\textit{N}=4}$超杨-米尔斯理论的非可逆对称性，可实现为相关顶点算子代数的外自同构。因此，带有非可逆对称扭转的$\boldsymbol{\textit{N}=4}$超杨-米尔斯理论的Schur指标和Macdonald指标，对应于带有外自同构扭转的相关顶点算子代数的（精炼）真空特征。我们从大$\boldsymbol{\textit{N}}$极限及匹配涉及局域算子电荷共轭的融合规则出发，为该提议提供了若干验证；“带电”Schur指标确实与外自同构扭转的真空特征匹配。
英文摘要
We argue that the non-invertible symmetry of $\mathcal{N}=4$ super Yang-Mills theory, obtained by combining S-duality, half-space gauging, and R-symmetry twist, is realized as an outer-automorphism of the associated vertex operator algebra. Hence, the Schur and Macdonald index of $\mathcal{N}=4$ super Yang-Mills theory with non-invertible symmetry twist corresponds to the (refined) vacuum character of the associated vertex operator algebra with the outer-automorphism twist. We provide a few checks of our proposal from the large-$N$ limit and by matching the fusion rules, which involve charge conjugation on local operators. The `charged' Schur index indeed matches the outer-automorphism-twisted vacuum character.
